Free Printable 8th Grade Algebra 1 Winter Final Review

1.

Classify the following: $\pi$

a)

Rational

b)

Irrational

2.

Select all that apply. What is a rational number ?

a)

A rational number is a number that can be written as a fraction.

b)

A rational number is a terminating decimal.

c)

A rational number is a decimal that repeats.

d)

A rational number is a decimal that goes on and on without repeating.

3.

Which of the following numbers is irrational?

a)

2.828427.....

b)

¾

c)

2

d)

-1.325

4.

Which of the following is a rational number?

a)

π

b)

2.82842712475...

c)

.56565656....

d)

3.16227766017...

5.

Classify the following: $\frac{3}{4}$

a)

Rational

b)

Irrational

6.

Classify the following: $0.525$

a)

Rational

b)

Irrational

7.

Select all Rational numbers

7/8 $\sqrt[]{13}$ 8.23481256... .45 7.343434... $-4\frac{3}{8}$

a)

7/8 .45 7.343434.... $-4\ \frac{3}{8}$

b)

$\sqrt[]{13}$ 8.23481256...

c)

none of them

d)

all of them

8.

Is the number $\sqrt[]{1225}$ rational or irrational? Explain

a)

Irrational since it is a square root

b)

Irrational since it is a non repeating decimal

c)

Rational since it equals a terminating decimal

d)

Rational since it repeats

9.

$\pi$ is irrational since it goes on forever with no pattern (it can not be made into a fraction)

a)

true

b)

false

10.

Which one is not a perfect square/irrational?

$\sqrt[]{49}\ \ \ \ \sqrt[]{121}\ \ \ \ \ \sqrt[]{15}\ \ \ \ \sqrt[]{4}$

a)

$\sqrt[]{49}$

b)

$\sqrt[]{121}$

c)

$\sqrt[]{4}$

d)

$\sqrt[]{15}$

11.

Simplify 5(2 - 7n)

a)

52 - 57n

b)

10 - 7n

c)

10 - 35n

d)

10 + 35n

12.

Simplify the expression:
6 + 2(7x - 3)

a)

12 + 7x

b)

14x

c)

14x + 3

d)

9 + 7x

13.

Simplify the Expression.
9z - 21 - 3z + 10

a)

Simplified

b)

9z - 21 - 7

c)

9z - 11 -3z

d)

6z - 11

14.

-8(3 + 4w)

a)

-5 + -4w

b)

-24 - 4w

c)

-24 + -32w

d)

-11 + -12w

15.

Simplify:

3(2x + 4) + 5x

a)

11x + 12

b)

11x + 4

c)

5x + 18

d)

6x + 9

16.

Simplify:

5(6n - 2) - 13

a)

11n - 20

b)

30n - 3

c)

30n - 23

d)

11n - 6

17.

Simplify:

10 + 4(2n + 3) -11n

a)

-3n + 22

b)

7n + 13

c)

19n + 17

d)

-3n + 13

18.

Simplify the expression

2k + 3b + 4k + 2b

a)

11kb

b)

6k + 5b

c)

5k + 6b

d)

None of the above

19.

Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.

a)

4m + 8

b)

8m - 4

c)

8m + 4

d)

4m - 8

20.

Translate this phrase into an algebraic expression.

The difference of 3 times a number and 7

Use the variable n to represent the unknown number.

a)

3 - 7n

b)

3n - 7

c)

3n + 7

d)

3 / 7n

21.

Translate this phrase into an algebraic expression.

2 times the difference of a number and 11

Use the variable t to represent the unknown number.

a)

2t - 11

b)

2(t - 11)

c)

2(t / 11)

d)

2 x t - 11

22.

Translate this phrase into an algebraic expression.

2 times the sum of a number and 15

Use the variable B to represent the unknown number.

a)

2(B+15)

b)

2B+15

c)

2B×15

d)

2×15B

23.

Write a word phrase to represent the following algebraic expression:

$\frac{z}{8}-9$

a)

the quotient of 8 and a number minus 9

b)

the product of 8 and a number minus 9

c)

the quotient of a number and 8 minus 9

d)

9 less than the quotient of a number and 8

24.

Write a word phrase to represent the following algebraic expression:

9n+1

a)

the quotient of 9 and a number plus 1

b)

the product of 9 and a number plus 1

c)

1 more than the quotient of 9 and a number

d)

1 more than the product of 9 and a number

25.

Write a word phrase to represent the following algebraic expression:

$\frac{12}{5t}$

a)

the quotient of 12 and 5 times a number

b)

the quotient of the product of 5 and a number and 12

c)

the quotient of 12 and the product of 5 and a number

d)

the quotient of 5 times a number and 12

26.

the difference of a number and six

a)

x + 6

b)

x - 6

c)

6 - x

d)

x/6

27.

4a + 3 = 15

a)

2

b)

4

c)

1

d)

3

28.

3(x+2) = 15

a)

13

b)

7

c)

4.33333

d)

3

29.

What value of k makes the equation $10k-7=7k-15$ true?

a)

$k=\frac{8}{3}$

b)

$k=-\frac{8}{3}$

c)

$k=\frac{22}{3}$

d)

$k=-\frac{22}{3}$

30.

What is the solution to the equation 3(2x - 5) = x + 10?

a)

9

b)

6

c)

8

d)

5

31.

You solve an equation and find that 7 = 9 in your final step. What does this mean?

a)

The equation has 1 solution.

b)

The equation has no solution.

c)

The equation has infinitely many solutions.

d)

The equation is an identity.

32.

Solve the equation -3(1 + 6x) = 14 - x.

a)

x = 1

b)

x = -1

c)

No solution

d)

All real numbers

33.

Write the phrase "the difference of 4 and a number" as a variable expression.

a)

x - 4

b)

4 - x

c)

x + 4

d)

4 + x

34.

What is the solution to the equation 3(5x + 4) - 20 = 13x - 4?

a)

2

b)

8

c)

-2

d)

4

35.

Write the following sentence as an equation: 7 less than twice a number is 17.

a)

7 - 2x = 17

b)

2(x - 7) = 17

c)

2x - 7 = 17

d)

2(7 - x) = 17

36.

Solve 2(y + 5) = 3(y - 8).

a)

-34

b)

14

c)

34

d)

-14

37.

Which of the following does not represent x - 5?

a)

The difference of a number and 5

b)

A number decreased by 5

c)

5 subtracted from a number

d)

A number less than 5

38.

Solve 8(x − 6) = −(x + 3).

a)

5

b)

-5

c)

7

d)

-7

39.

What is the solution to the equation 6x + 12 = 2x + 4(x + 3)?

a)

x = 2

b)

x = 0

c)

No solution

d)

All real numbers

40.

$3\left(x+4\right)=3\left(x-8\right)$

a)

one solution

b)

no solution

c)

infinite solutions

41.

$-2\left(x+1\right)=x-3x-2$

a)

one solution

b)

no solution

c)

infinite solutions

42.

$\frac{1}{2}\left(x+4\right)=\frac{1}{2}\left(x-8\right)$

a)

one solution

b)

no solution

c)

infinite solutions

43.

Determine the type of solution you will have if you get

-5=-5

a)

one solution

b)

infinitely many solutions

c)

no solution

d)

I don't know. I need to study.

44.

$\ u\ =\ bak\$ Solve for a

a)

$a=\frac{u}{bk}$

b)

$a\ =\ \frac{bk}{u}$

c)

$a\ =\ -\frac{bk}{u}$

d)

$a=-\frac{u}{bk}$

45.

$Given\ ax-b=c,\ solve\ for\ x.\$

a)

$x\ =\ \frac{c+b}{a}$

b)

$x\ =\ \frac{c-b}{a}$

c)

$x\ =\ \frac{a+b}{c}$

d)

$x\ =\ \frac{c+a}{b}$

46.

$Given\ d=rt,\ solve\ for\ r.\$

a)

$r=\frac{t}{d}$

b)

$t\ =\ \frac{d}{r}$

c)

$d=\frac{r}{t}$

d)

$r=\frac{d}{t}$

47.

$Given\ V=lwh,\ solve\ for\ l.$

a)

$l=\frac{Vw}{h}$

b)

$l=\frac{V}{wh}$

c)

$l=\frac{Vh}{w}$

d)

$l=\frac{wh}{V}$

48.

$Solve:\ C=2\pi r,\ for\ r$

a)

$r=\frac{C}{2\pi}$

b)

$r=C+2\pi$

c)

$r=C-2\pi$

d)

$r=2\pi C$

49.

$Given\ 8x+4y=16,\ solve\ for\ y.$

a)

$y=-2x+4$

b)

$y=-8x+16$

c)

$y=2x-4$

d)

$y=-8x+12$

50.

$Solve\ y\ =\ mx\ +\ b\ for\ x.$

a)

$x=\frac{\left(y-b\right)}{m}$

b)

$x\ =\ y-\frac{b}{m}$

c)

$x=\frac{y}{m}-b$

51.

Solve the inequality.

30 + n ≥ 50

a)

n ≥ 50

b)

x ≥ 80

c)

n ≤ 30

d)

n ≥ 20

52.

Will my dot be colored in?
5 ≥ x

a)

Yes

b)

No

53.

When you graph an inequality, you used a closed dot when you use which symbols?

a)

≤, ≥

b)

<, >

c)

≤, <

d)

≥, >

54.

Solve:
6x+10>5x-12

a)

x>2

b)

x<2

c)

x<-22

d)

x>-22

55.

Which graph matches the inequality
k < 3?

a)

A

b)

B

c)

C

d)

D

56.

14 < -2a + 6 - 2a

a)

a > -2

b)

a < -2

c)

a > 5

d)

a < -5

57.

4(2a + 3) < 3(a - 1)

a)

a < -3

b)

a > -3

c)

a < 3

d)

a > 3

58.

a)

A

b)

B

c)

C

d)

D

59.

a)

A

b)

B

c)

C

d)

D

60.

a)

A

b)

B

c)

C

d)

D

61.

a)

A

b)

B

c)

C

d)

D

62.

a)

A

b)

B

c)

C

d)

D

63.

a)

A

b)

B

c)

C

d)

D

64.

a)

A

b)

B

c)

C

d)

D

65.

Write the following in interval notation

x < 8

a)

[8, ∞)

b)

(8, -∞)

c)

(-∞, 8]

d)

(-∞, 8)

66.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

67.

Write the following in interval notation
x ≥ 100

a)

(0, 100]

b)

(∞, 100]

c)

[100, ∞)

d)

(∞, 100)

68.

Convert into its interval notation:

$0\le x\le3$

a)

[0, 3]

b)

(0, 3)

c)

[0, 3)

d)

(0, 3]

69.

Convert into its interval notation:

$5<x\le11$

a)

(5, 11]

b)

[5, 11]

c)

(5, 11)

d)

[5, 11)

70.

Look at the Graph. Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

71.

Look at the picture. Which number line corresponds to [-2, 5]?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

72.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

73.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

74.

Convert this internal notation to inequality notation.

$\left(-\infty,0\right]$

a)

$x<0$

b)

$x\le0$

c)

$x>0$

75.

Look at the picture. Select the correct interval notation for the given number line.

a)

(-∞, -8) U (-4, ∞)

b)

(-∞, -8] U [-4, ∞)

c)

(-8, -4)

d)

[-8, -4]

76.

Look at the picture. Which graph best represents the solution set (-∞, -2) U (5, ∞)?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

77.

Do the segment lengths 9, 12, and 15 form a right triangle?

a)

Yes

b)

No

78.

Find the length of the missing side

a)

17

b)

15

c)

22

d)

13

79.

Find the length of the missing side

a)

20

b)

68

c)

16

d)

80

80.

Is this a right triangle

a)

Yes

b)

No

81.

Find the length of the side indicated in the triangle below:

a)

A

b)

B

c)

C

d)

D

82.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

83.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

84.

A coordinate plane is shown with labeled points.

What is the distance between point A and point B on the coordinate plane?

a)

5

b)

6

c)

10

d)

14

85.

Find the distance between these two points. Round to the nearest tenth.

a)

3.3 units

b)

7 units

c)

8.1 units

d)

11 units

86.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

87.

Simplify the following radical: √24

a)

2√6

b)

4√6

c)

2√12

d)

3√8

88.

Simplify the following radical: √300

a)

3√10

b)

2√150

c)

100√3

d)

10√3

89.

Simplify:
√96

a)

16√6

b)

6√16

c)

9√6

d)

4√6

90.

$\sqrt{63}$

a)

$9\sqrt{7}$

b)

$6\sqrt{2}$

c)

$7\sqrt{6}$

d)

$3\sqrt{7}$

91.

$4\sqrt{6}\cdot\sqrt{3}$

a)

$4\sqrt{9}$

b)

$\sqrt{72}$

c)

$4\sqrt{18}$

d)

$12\sqrt{3}$

92.

$5\sqrt{2}\cdot4\sqrt{10}$

a)

$20\sqrt{20}$

b)

$10\sqrt{40}$

c)

$40\sqrt{5}$

d)

$9\sqrt{13}$

93.

Simplify 8√80

a)

8√2

b)

32√5

c)

-16√2

d)

10√6

94.

Simplify 3√72

a)

-5√3

b)

40√2

c)

-32√7

d)

18√2

95.

Simplify 4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

96.

Simplify:

$-3\sqrt[]{12}$

a)

$-6\sqrt[]{3}$

b)

$-3\sqrt[]{6}$

c)

$-12\sqrt[]{3}$

d)

$6\sqrt[]{3}$

97.

Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

a)

21 cubic inches

b)

63 cubic inches

c)

66 cubic inches

d)

198 cubic inches

98.

The radius in this cylinder is 6.4 cm. True or False?

a)

True

b)

False

99.

Calculate the volume of this cylinder. Use the formula $v=\pi r^2h$ and $\pi=3.14$ .

a)

$v=150.72\ ft^3$

b)

$v=602.88\ ft^3$

c)

$v=1,808.64\ ft^3$

d)

$v=301.44\ ft^3$

100.

A cylinder has a diameter of 12 cm and a height of 9 cm. Which measurement is closest to the volume of the cylinder?

a)

1527

b)

4072

c)

1018

d)

3054

101.

A sphere has a radius of 7 ft. What is closest to the volume of the sphere?

a)

1436.76

b)

10057.3

c)

205.25

d)

51.31

102.

What is the total surface area of the cylinder to the nearest square inch?

a)

625 in²

b)

1300 in²

c)

1046 in²

d)

414 in²

103.

Find the surface area

a)

140.25 cm²

b)

439.82 cm²

c)

219.91 cm²

d)

192.25 cm²

104.

A paper party hat, like the one shown, has a slant height of 6 inches and a radius of 5 inches. How many square inches of cardboard would be needed to create this hat?

a)

94.25 in.²

b)

172.79 in.²

c)

50 in.²

d)

22.5 in.²

105.

Find the total surface area of the cone. Round to the nearest tenth.

a)

37.7 m²

b)

50.3 m²

c)

75.4 m²

d)

25.1 m²

106.

Find the surface area of the sphere, given diameter is 10 in.

a)

314.16 in²

b)

314 in²

c)

166.67 in²

d)

521.24 in²

107.

For a sphere with a radius of 11in, what is the Surface Area?

a)

506.59 in²

b)

16,717.36 in²

c)

5,572.45 in²

d)

1,519.76m in²

108.

What is the surface area of the sphere?

a)

50.266 ft²

b)

25.133 ft²

c)

100.512 ft²

d)

4 ft²

109.

Find the slope between the two given points: (-2,1) and (5,7)

a)

7/6

b)

2

c)

6/7

d)

-2

110.

Find the slope:
(-1,-9) and (5, -6)

a)

-15/4

b)

1/2

c)

-3/6

d)

11/3

111.

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 3 y-intercept: (0,3/2)

d)

slope: 3/2 y-intercept: (0,5)

112.

Find the slope of the line between the points: (-5, 6) and (-5, -1)

a)

m = -7

b)

m = $\frac{10}{7}$

c)

m = undefined

d)

m = 0

113.

What is the equation of a line with a slope of 4 and a y-intercept of 2?

a)

y = -4x + 2

b)

y = -2x + 4

c)

y = 4x + 2

d)

y = 2x + 4

114.

What is the equation of a line when m = -3 and b = 5?

a)

y = -3x + 5

b)

y = -3x - 5

c)

y = 5x + 3

d)

y = -5x - 3

115.

Identify the y-intercept of the equation
y=2x+5

a)

2

b)

5

116.

Identify the slope of the Equation
y=5x+3

a)

5

b)

3

117.

What is the equation of a line with a slope of 4 and a y-intercept of 2?

a)

y = -4x + 2

b)

y = -2x + 4

c)

y = 4x + 2

d)

y = 2x + 4

8th Grade Algebra 1 Winter Final Review

Total questions: 117

Worksheet time: 20hrs 30mins

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